Testing the Number of Components in Normal Mixture Regression Models

Testing the number of components in finite normal mixture models is a long-standing challenge because of its nonregularity. This article studies likelihood-based testing of the number of components in normal mixture regression models with heteroscedastic components. We construct a likelihood-based test of the null hypothesis of m0 components against the alternative hypothesis of m0 + 1 components for any m0. The null asymptotic distribution of the proposed modified EM test statistic is the maximum of m0 random variables that can be easily simulated. The simulations show that the proposed test has very good finite sample size and power properties. Supplementary materials for this article are available online.